Governor Deval Patrick said Thursday he is open to the state Senate’s transportation financing plan, comments that could end a tense standoff between the governor and legislative leaders, who have not spoken in weeks.

The governor said he believes the $805 million bill proposed by Senate leaders could serve as a middle ground between the $1 billion tax increase for transportation he wants and the $500 million tax hike the House passed this week.

Patrick had vowed to veto the House bill, calling it woefully insufficient.

But he praised the Senate legislation, which includes the same tax increases as the House bill while boosting transportation further by redirecting money from other parts of the state budget and imposing a new fee on utilities.

“Well, it’s definitely moving in the right direction,” Patrick told reporters in a State House hallway. “It’s a very, very hopeful movement in the right direction.”

Patrick’s shift in rhetoric, from harsh criticism of the House bill to open interest in the Senate plan, seemed ­designed to de-escalate the acrimony between the three most powerful players on Beacon Hill: the governor, Senate President Therese Murray, and House Speaker Robert A. ­DeLeo, all of them Democrats.

Just hours before Patrick’s comments Thursday, Murray said she had not spoken to the governor in three weeks and was upset about the rhetoric he used to denounce the initial $500 million transit plan that she and House leaders proposed last week.

Several hurdles remain before there is a breakthrough, however.

It is not clear whether House leaders would agree to a deal based on the more expensive Senate plan. A spokesman for DeLeo released a statement Thursday saying only that “the House awaits passage of the Senate transportation finance bill,’’ which is currently scheduled for debate on Saturday.

In addition, Patrick aides said the governor has not ­declared his full support for the Senate bill because he is still trying to assess whether it can generate enough revenue to support the ambitious transit projects he wants to initiate. Patrick’s agenda includes rail routes from Boston to Fall River and New Bedford and from Pittsfield to New York City.

“We’re trying to check to see whether the dollars are real,” Patrick said.

The governor and legislative leaders have insisted for months that they want to hammer out an agreement to ­increase funding for the transit system and stave off looming MBTA fare increases. But they have not been able to agree on the size and scope of the legislation.

The governor has been pushing for a $1.9 billion tax hike — $1 billion for transportation and $900 million for education — calling it essential for the state’s economic growth, while legislative leaders have said they want a smaller tax hike aimed at shoring up the MBTA and regional transit author­ities.

Patrick had called the Legislature’s framework “a return to an old way of doing business” and “the same short-term fiscal shell game that got us the Big Dig and the mess that followed.”

That characterization irritated Murray. “You have to be careful when you speak, and the rhetoric and the words that you use, if you want to move things ahead,” she told reporters after speaking to the ­Greater Boston Chamber of Commerce.

Asked if the governor was too harsh, she said, “I think people felt that.”

Hours later, the governor, sounding ready to make amends, made a point of praising Murray for going beyond her initial $500 million proposal.

“You see that the Senate has moved to a different place than was announced back then,” said Patrick. “It was about kicking the can down the road. But I think there are a lot of people in the Legislature – and, I think, including the Senate president — who don’t want to kick the can down the road, and I think that’s one of the reasons we’ve seen the movement on the ­Senate side.”

The Senate plan, like the House bill, would increase the state gas tax from 21 cents to 24 cents per gallon and tie further increases to inflation beginning in 2015. It would also raise the cigarette tax by $1.00 per pack and impose new taxes on certain kinds of software.

But the Senate bill includes additional sources of revenue.

It would raise another $40 million by requiring utility companies to pay for infrastructure, such as light poles, on state highways, and take another $80 million for transportation from an underground storage tank cleanup fund.

All told, the bill is designed to ramp up funding for transportation over the next five years, from an additional $265 million this year to an additional $805 million in 2017.

Thomas M. McGee, a Lynn Democrat who is Senate chairman of the Transportation Committee, said he was hopeful that Patrick’s praise for the ­Senate proposal will help thaw relations between the governor and the Legislature.

“In politics, sometimes our passions come out, clearly,” he said. “But in the long run, I think we all have the same goal in mind, and I really am optimistic we can continue to move the issue forward.”

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